Gérard TAILLE wrote:
It seems there is some wording problems especially in your first point
1. Determine for every string of stones if they can be captured, and not reestablished with stones that can not be captured, and declare these stones to be ALIVE.
Anyway maybe can you show your proposal on the very first L&D example 1
- Click Here To Show Diagram Code
[go]$$B
$$ +---------------------–-
$$ | . X X O . . .
$$ | O X X O . . .
$$ | X O O O . . .
$$ | X X X . . . .
$$ | . . . . . . .[/go]
Sorry about the bad wording. My intention was to convey the general idea.
It was the intention that step 1 was the regular j89 determination of alive status. In example 1 all the stones are alive, and there is nothing different from the non-iterative process.
I notice that I should have said for step 3 that the dead stones are to be removed if they are surrounded only by dead stones of the same color or alive stones of the other color. I hope this is understandable enough if a little bit imprecise.
Another issue is the (deliberately) imprecise treatment of removed dead stones in step 3, I think a little bit more needs to be said about how to treat them in later iteration. For now I am assuming (somewhat contrary to what I said before) that they are left in-place, can be captured by the other color, but the same color can not play new stones in place of captured stones that were marked as dead.
The first example of iterative application would be example 8, so I will try to demonstrate with this example.
- Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . .
$$ | O O . . . . .
$$ | X O . . . . .
$$ | . X O O O . .
$$ | X X X X O . .
$$ | O X . X O . .
$$ | . O X O X . .
$$ | O O O O X . .
$$ | . O X X X . .
$$ | O O X . . . .
$$ | X X X . . . .
$$ | . . . . . . .[/go]
Iteration 1Step 1 determination of alive status.
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[go]$$B step 1
$$ | . . . . . . .
$$ | O O . . . . .
$$ | 1 O . . . . .
$$ | . 1 O O O . .
$$ | 1 1 1 1 O . .
$$ | 2 1 . 1 O . .
$$ | . 4 1 4 X . .
$$ | 4 4 4 4 X . .
$$ | . 4 X X X . .
$$ | 4 4 X . . . .
$$ | X X X . . . .
$$ | . . . . . . .[/go]
Statuses:

dead - per the original rules

dead - assuming double-ko "abuse" because black can capture this stone in a cycle.

alive - per the original rules
This would be sufficient, if double-ko "abuse" is ignored, but here the loop continues.
In step 2 the alive white stones are removed from further consideration, marked with x-es.
- Click Here To Show Diagram Code
[go]$$B step 2
$$ | . . . . . . .
$$ | O O . . . . .
$$ | X O . . . . .
$$ | . X O O O . .
$$ | X X X X O . .
$$ | O X . X O . .
$$ | . P X P X . .
$$ | P P P P X . .
$$ | . P X X X . .
$$ | P P X . . . .
$$ | X X X . . . .
$$ | . . . . . . .[/go]
In step 3 there is one black stone to mark as dead.
- Click Here To Show Diagram Code
[go]$$B step 3
$$ | . . . . . . .
$$ | O O . . . . .
$$ | A O . . . . .
$$ | . X O O O . .
$$ | X X X X O . .
$$ | O X . X O . .
$$ | . P X P X . .
$$ | P P P P X . .
$$ | . P X X X . .
$$ | P P X . . . .
$$ | X X X . . . .
$$ | . . . . . . .[/go]
Iteration 2
- Click Here To Show Diagram Code
[go]$$B step 1
$$ | . . . . . . .
$$ | O O . . . . .
$$ | A O . . . . .
$$ | . 1 O O O . .
$$ | 1 1 1 1 O . .
$$ | 2 1 . 1 O . .
$$ | . P 1 P X . .
$$ | P P P P X . .
$$ | . P X X X . .
$$ | P P X . . . .
$$ | X X X . . . .
$$ | . . . . . . .[/go]
Now that some stones fixed as dead or alive we have the following statuses for the remaining stones:

dead

alive
In step 2 the alive white stones are removed from further consideration, marked with x-es.
- Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . .
$$ | O O . . . . .
$$ | A O . . . . .
$$ | . X O O O . .
$$ | X X X X O . .
$$ | P X . X O . .
$$ | . P X P X . .
$$ | P P P P X . .
$$ | . P X X X . .
$$ | P P X . . . .
$$ | X X X . . . .
$$ | . . . . . . .[/go]
In step 3 the dead black stones that are surrounded by alive white stones and dead black stones are marked as dead.
- Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . .
$$ | O O . . . . .
$$ | A O . . . . .
$$ | . A O O O . .
$$ | A A A A O . .
$$ | P A . A O . .
$$ | . P A P X . .
$$ | P P P P X . .
$$ | . P X X X . .
$$ | P P X . . . .
$$ | X X X . . . .
$$ | . . . . . . .[/go]
Iteration 3There are no stones left relating to the example so the loop terminates with no chances from the previous diagram.
Status at end of the loop
- Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . .
$$ | O O . . . . .
$$ | 1 O . . . . .
$$ | . 1 O O O . .
$$ | 1 1 1 1 O . .
$$ | 2 1 . 1 O . .
$$ | . 2 1 2 X . .
$$ | 2 2 2 2 X . .
$$ | . 2 X X X . .
$$ | 2 2 X . . . .
$$ | X X X . . . .
$$ | . . . . . . .[/go]

dead

alive
I hope this explains the general concept, even if I have not come up with a precise enough formulation yet.